Why is the differential of a constant zero?
Any constant (say k) can be rewritten as kx0 since x0=1. When you differentiate this, the 0 which is the power of the x term gets dragged to the front and is multiplied with the rest of the expression (according to the short-hand differential method). So if f(x) = kx0 is differentiated, we get f '(x) = 0kx-1 = 0.
JC
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